According to this study, no.
We conclude that no statistically significant overall association can be detected between milk and dairy product intake and symptoms of mucus production in healthy adults, either asymptomatic or symptomatic, with rhinovirus infection.
It seems that you're already aware of this given your comment:
I've also read elsewhere ...
In sinusitis, there may already be a negative pressure in the sinuses (nih.gov).
One problem is that in sinusitis the openings that connect the nasal cavity and sinuses are usually clogged, so the attempt to create a pressure difference might be quite hard.
I'm not aware of any published experiments on this topic, but as suggested in one comment: the one ...
The following is for adults:
Relationship between milk intake and mucus production in adult volunteers challenged with rhinovirus-2.
In individuals inoculated with the common cold virus, milk intake was
not associated with increased nasal secretions, symptoms of cough,
nose symptoms or congestion.